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Pierre Melchior - One of the best experts on this subject based on the ideXlab platform.
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Improvements on flat output characterization for fractional systems
Fractional Calculus and Applied Analysis, 2015Co-Authors: Stéphane Victor, Pierre MelchiorAbstract:In trajectory planning, Flatness is used to compute inputs generating suitable trajectories, without using any integration. The Flatness property of linear controllable time-invariant fractional systems is studied. The formalism of polynomial matrix of the fractional differential operator is used leading to the characterization of fractionally flat outputs. The so-called defining matrices, which are transformations that express all system variables in function of the fractionally flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Flatness of fractional systems is then applied to the trajectory planning of a real thermal experiment. MSC 2010 : 26A33, 34A08, 60G22
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Computation of flat outputs for fractional systems: a Thermal Application
2013Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:In trajectory planning, Flatness is used to compute inputs generating suitable trajectories, without using any integration. The extension of linear flat outputs to linear controllable time-invariant fractional systems is put forward by means of polynomial matrix formalism, leading to the notion of fractional Flatness. The so-called defining matrices, which are transformations that express all system variables in function of the flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Fractional Flatness is then applied to the trajectory planning of a real thermal experiment.
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Robust path tracking using Flatness for fractional linear MIMO systems: A thermal application
Computers and Mathematics with Applications, 2010Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:This paper deals with robust path tracking using Flatness principles extended to fractional linear MIMO systems. As soon as the path has been obtained by means of the fractional Flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for fractional linear SISO systems using a transfer function approach. For fractional systems, especially in MIMO, developments are still to be made. Throughout this paper, Flatness principles are applied using polynomial matrices for fractional linear MIMO systems. To illustrate the robustness performances, a third-generation multi-scalar CRONE controller is compared to a PID one.
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Flatness control for linear fractional {MIMO} systems: thermal application
2008Co-Authors: Stéphane Victor, Dominique Nelson Gruel, Pierre Melchior, Alain OustaloupAbstract:This paper concerns the application of Flatness principle to linear fractional MIMO systems. As soon as the path has been obtained by fractional Flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for LTI systems. On previous works on fractional systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply Flatness principle using polynomial matrices for linear fractional MIMO systems with a robust path tracking.
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Flatness principle extension to linear fractional MIMO systems: Thermal application
MELECON 2008 - The 14th IEEE Mediterranean Electrotechnical Conference, 2008Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:This paper concerns the application of Flatness principle to fractional MIMO systems in the pseudo-state-space representation. The aim here is to compute linear flat outputs for linear controllable time-invariant systems in polynomial matrix form. The defining matrices expressed with the system variables in terms of a linear flat output and its derivatives define the kernel of a polynomial matrix. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed. Several developments have been made for LTI systems, however concerning fractional differentiation systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply Flatness principle using polynomial matrices for linear fractional MIMO systems.
Stéphane Victor - One of the best experts on this subject based on the ideXlab platform.
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Improvements on flat output characterization for fractional systems
Fractional Calculus and Applied Analysis, 2015Co-Authors: Stéphane Victor, Pierre MelchiorAbstract:In trajectory planning, Flatness is used to compute inputs generating suitable trajectories, without using any integration. The Flatness property of linear controllable time-invariant fractional systems is studied. The formalism of polynomial matrix of the fractional differential operator is used leading to the characterization of fractionally flat outputs. The so-called defining matrices, which are transformations that express all system variables in function of the fractionally flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Flatness of fractional systems is then applied to the trajectory planning of a real thermal experiment. MSC 2010 : 26A33, 34A08, 60G22
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Computation of flat outputs for fractional systems: a Thermal Application
2013Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:In trajectory planning, Flatness is used to compute inputs generating suitable trajectories, without using any integration. The extension of linear flat outputs to linear controllable time-invariant fractional systems is put forward by means of polynomial matrix formalism, leading to the notion of fractional Flatness. The so-called defining matrices, which are transformations that express all system variables in function of the flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Fractional Flatness is then applied to the trajectory planning of a real thermal experiment.
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Robust path tracking using Flatness for fractional linear MIMO systems: A thermal application
Computers and Mathematics with Applications, 2010Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:This paper deals with robust path tracking using Flatness principles extended to fractional linear MIMO systems. As soon as the path has been obtained by means of the fractional Flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for fractional linear SISO systems using a transfer function approach. For fractional systems, especially in MIMO, developments are still to be made. Throughout this paper, Flatness principles are applied using polynomial matrices for fractional linear MIMO systems. To illustrate the robustness performances, a third-generation multi-scalar CRONE controller is compared to a PID one.
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Flatness control for linear fractional {MIMO} systems: thermal application
2008Co-Authors: Stéphane Victor, Dominique Nelson Gruel, Pierre Melchior, Alain OustaloupAbstract:This paper concerns the application of Flatness principle to linear fractional MIMO systems. As soon as the path has been obtained by fractional Flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for LTI systems. On previous works on fractional systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply Flatness principle using polynomial matrices for linear fractional MIMO systems with a robust path tracking.
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Flatness principle extension to linear fractional MIMO systems: Thermal application
MELECON 2008 - The 14th IEEE Mediterranean Electrotechnical Conference, 2008Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:This paper concerns the application of Flatness principle to fractional MIMO systems in the pseudo-state-space representation. The aim here is to compute linear flat outputs for linear controllable time-invariant systems in polynomial matrix form. The defining matrices expressed with the system variables in terms of a linear flat output and its derivatives define the kernel of a polynomial matrix. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed. Several developments have been made for LTI systems, however concerning fractional differentiation systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply Flatness principle using polynomial matrices for linear fractional MIMO systems.
Howard R Huff - One of the best experts on this subject based on the ideXlab platform.
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wafer Flatness modeling for scanning steppers
Proceedings of SPIE the International Society for Optical Engineering, 1996Co-Authors: Randal K Goodall, Howard R HuffAbstract:Model-based analysis is used to explain previous observations regarding the distributional form and numeric relationships of several key lithographic Flatness quality metrics for silicon wafers. The dominant relationships are controlled by longer wavelength (tens of millimeters) surface topography, while the distribution shapes are controlled by shorter wavelength (few millimeters) topography. A lithographic Flatness modeling framework is introduced which can provide guidance for specification of silicon wafer Flatness for ULSI IC products. New site Flatness models show that, compared to a full-field stepper, a scanning stepper can effect improved Flatness performance from wafers of similar quality.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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correlation of 150 mm p p epitaxial silicon wafer Flatness parameters for deep submicron applications
Journal of The Electrochemical Society, 1993Co-Authors: Howard R Huff, G H Popham, R. W. PotterAbstract:Experimental data for 426 P/P + epitaxial wafers from two suppliers are presented for both front-surface and back-surface site Flatness parameters SFQR, SFQD, SBIR, SBID and global data GFLR, GFLD, GF3R, GF3D, GBIR, taper, bow, warp, and sori. Correlations and recommendations among the various Flatness parameters are presented to gain insight into the characteristic Flatness parameters required for an accurate description of wafer Flatness. The recommended Flatness parameters for measurement are GFLR, GBIR, SFQR, and warp
Alain Oustaloup - One of the best experts on this subject based on the ideXlab platform.
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Computation of flat outputs for fractional systems: a Thermal Application
2013Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:In trajectory planning, Flatness is used to compute inputs generating suitable trajectories, without using any integration. The extension of linear flat outputs to linear controllable time-invariant fractional systems is put forward by means of polynomial matrix formalism, leading to the notion of fractional Flatness. The so-called defining matrices, which are transformations that express all system variables in function of the flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Fractional Flatness is then applied to the trajectory planning of a real thermal experiment.
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Robust path tracking using Flatness for fractional linear MIMO systems: A thermal application
Computers and Mathematics with Applications, 2010Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:This paper deals with robust path tracking using Flatness principles extended to fractional linear MIMO systems. As soon as the path has been obtained by means of the fractional Flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for fractional linear SISO systems using a transfer function approach. For fractional systems, especially in MIMO, developments are still to be made. Throughout this paper, Flatness principles are applied using polynomial matrices for fractional linear MIMO systems. To illustrate the robustness performances, a third-generation multi-scalar CRONE controller is compared to a PID one.
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Flatness control for linear fractional {MIMO} systems: thermal application
2008Co-Authors: Stéphane Victor, Dominique Nelson Gruel, Pierre Melchior, Alain OustaloupAbstract:This paper concerns the application of Flatness principle to linear fractional MIMO systems. As soon as the path has been obtained by fractional Flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for LTI systems. On previous works on fractional systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply Flatness principle using polynomial matrices for linear fractional MIMO systems with a robust path tracking.
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Flatness principle extension to linear fractional MIMO systems: Thermal application
MELECON 2008 - The 14th IEEE Mediterranean Electrotechnical Conference, 2008Co-Authors: Stéphane Victor, Pierre Melchior, Alain OustaloupAbstract:This paper concerns the application of Flatness principle to fractional MIMO systems in the pseudo-state-space representation. The aim here is to compute linear flat outputs for linear controllable time-invariant systems in polynomial matrix form. The defining matrices expressed with the system variables in terms of a linear flat output and its derivatives define the kernel of a polynomial matrix. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed. Several developments have been made for LTI systems, however concerning fractional differentiation systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply Flatness principle using polynomial matrices for linear fractional MIMO systems.
Gilles Millerioux - One of the best experts on this subject based on the ideXlab platform.
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Flatness and submersivity of discrete-time dynamical systems
IEEE Control Systems Letters, 2020Co-Authors: Philippe Guillot, Gilles MilleriouxAbstract:This paper addresses Flatness of discrete-time systems called difference Flatness. A definition of Flatness, that encompasses the standard ones, in particular backward and forward difference Flatness, is introduced. It also allows to cope with systems which are not necessarily controllable or submersive. Besides, it considers nonlinear dynamical systems defined on general sets (without necessary special structures) which can be either continuous or discrete. Based on this definition, a result is established and stipulates that a flat and submersive nonlinear system is fully reachable (which is equivalent to fully controllable). Next, the special case of linear systems is considered leading to a necessary and sufficient condition.
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Flatness of Switched Linear Discrete-Time Systems
IEEE Transactions on Automatic Control, 2009Co-Authors: Gilles Millerioux, Jamal DaafouzAbstract:This note is devoted to Flatness for switched linear discrete-time systems. For this class of hybrid systems, algebraic conditions are derived to check whether a given output is flat. Then, a feedforward Flatness-based control strategy for trajectory tracking is proposed.
